5 edition of Riemann surfaces by way of complex analytic geometry found in the catalog.
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This book establishes the basic function theory and complex geometry of Riemann surfaces, both open and compact. Many of the methods used in the book are adaptations and simplifications of methods from the theories of several complex variables and complex analytic geometry and would serve as excellent training for mathematicians wanting to work in complex analytic by: This book establishes the basic function theory and complex geometry of Riemann surfaces, both open and compact.
Many of the methods used in the book are adaptations and simplifications of methods from the theories of several complex variables and complex analytic geometry.
Riemann surfaces by way of complex analytic geometry / Dror Varolin. — (Graduate studies in mathematics ; v. ) Includes bibliographical references and index. ISBN (alk. paper) 1. Riemann surfaces. Functions of complex variables.
Geometry, Analytic. Title. Series. QAV37 —dc23 Riemann Surfaces by Way of Complex Analytic Geometry About this Title. Dror Varolin, Stony Brook University, Stony Brook, NY.
Publication: Graduate Studies in Mathematics Publication Year Volume ISBNs: (print); (online)Cited by: Get this from a library. Riemann surfaces by way of complex analytic geometry. [Dror Varolin]. Riemann Surfaces by Way of Complex Analytic Geometry 作者: Dror Varolin 出版社: American Mathematical Society 出版年: 页数: 定价: USD 装帧: Hardcover 丛书: Graduate Studies in Mathematics.
The theory of Riemann surfaces begins with Chapter 4. This chapter covers the basic deﬁnitions of such surfaces and the analytic functions on them. Elementary results such as the Riemann-Hurwitz formula for the branch points are discussed and several examples of surfaces and analytic functions deﬁned on them are presented.
Narasimhan-Nievergelt's Complex Analysis in One Variable is exactly the book you want. It is completely geometric and will introduce you, starting from scratch, not only to Riemann surfaces but also to the theory or holomorphic functions of several variables, covering spaces, cohomology.
Frances Kirwan's book Complex Algebraic Curves has two really nice chapters on Riemann Surfaces and over all the level of the book is pretty decent to start with. The book is intended to be accessible to advanced undergraduates so perhaps not as advanced as you'd like, but it is.
Cavalieri, Miles - Riemann Surfaces and Algebraic Curves, A First Course in Hurwitz Theory (): as the title suggests, it is an approach to Complex Algebraic Curves with strong focus on Hurwitz Theory.
The basics of Riemann surfaces are layed out and then the author moves on to the counting. Chapter 1. Book Overview 1 § Behold, the Torus.
1 § Gluing Polygons 3 § Drawing on a Surface 5 § Covering Spaces 8 § Hyperbolic Geometry and the Octagon 9 § Complex Analysis and Riemann Surfaces 11 § Cone Surfaces and Translation Surfaces 13 § The Modular Group and the Veech Group 14 § Moduli Space.
This book is by far much more than just another text on algebraic curves, among several others, for it offers many new and unique features one prominent feature is provided by the fact that the analytic viewpoint (Riemann surfaces) and the algebraic aspect (projective curves) are discussed in a well-balanced fashion Reviews: Riemann Surfaces by Way of Complex Analytic Geometry Page xvi (17 of ) xvi Preface.
name: designer sections.) A reasonable example of (ii) is provided by a number. of the results proved in Chapter 8, such as the Mittag-Leffler Theorem. An abstract Riemann surface is a surface (a real, 2-dimensional mani-fold) with a ‘good’ notion of complex-analytic functions.
The most important examples, and the rst to arise, historically, were the graphs of multi-valued analytic functions: Moral de nition: A (concrete) Riemann surface in C2 is a locally closed subset which. Example The most trivial example of a Riemann surface is of course the complex plane it self with the identity coordinate chart C.
To see this let fUj: j 2 Jg be an open cover of the complex plane and let `j send each Uj to itself. From this the result should be obvious.
Also any open subset of Cor Riemann surface is also a Riemann surface. 11/3/ ] The theory of Riemann surfaces, and complex analysis in general, is a privileged part of mathematics: It is analysis and geometry, of course, but it is also algebra and differential equations, and a source of problems for many other branches of the mathematical tree.
There are many wonderful books on Riemann surfaces, with various approaches and emphases that. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topologycan be quite different.
For example, they can look like a sphereor a torusor several sheets glued together. Riemann surfaces by way of complex analytic geometry Subject: Providence, RI, American Math. Soc., Keywords: Signatur des Originals (Print): RR (). Digitalisiert von der TIB, Hannover, Created Date: 1/14/ AM.
Functions on Riemann surfaces 70 3. Degree and genus 72 4. Riemann surfaces as quotients 73 5. Elliptic functions 76 Chapter 5. Analytic continuation, covering surfaces, and algebraic functions 81 1. Analytic continuation 81 2. The unramiﬂed Riemann surface of an analytic germ 86 3. The ramiﬂed Riemann surface of an analytic germ 88 4.
The moduli problem is to describe the structure of the spaceof isomorphism classes of Riemann surfaces of a giventopological type. This space is known as the modulispace and has been at the center of pure mathematics formore than a hundred years.
This book begins by presenting the Kodaira-Spencer theory in its original naive form in Chapter 1 and introduces readers to moduli theory from the viewpoint of complex analytic r 2 briefly outlines the theory of period mapping and Jacobian variety for compact Riemann surfaces, with the Torelli theorem as a goal.Elliptic functions and Riemann surfaces played an important role in nineteenth-century mathematics.
At the present time there is a great revival of interest in these topics not only for their own sake but also because of their applications to so many areas of mathematical research from group theory and number theory to topology and differential equations.Download Riemann surfaces, dynamics and geometry Course Notes Download free online book chm pdf / Mathematics Books / Geometry Books / Riemann surfaces, dynamics and geometry Course Notes inscribed angles, Higher geometry, Classification of isometries of the plane, A bit of analytic geometry in 2 and 3 dimensions, The sphere and.